On the Parameterized Complexity of the Maximum Edge Coloring Problem

Abstract: We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q>1 and a graph G, the goal is to find a coloring of the edges of G with the maximum number of colors such that every vertex of the graph sees at most q colors. This problem is NP-hard for q>1, and has been well-studied from the point of view of approximation. Our main focus is the case when q=2, which is already theoretically intricate and practically relevant. We show fixed-parameter tractable algorithms for both the standard and the dual parameter, and for the latter problem, the result is based on a linear vertex kernel.